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A233907 9*binomial(7*n+9, n)/(7*n+9). 6

%I

%S 1,9,99,1218,16065,222138,3178140,46656324,698868216,10639125640,

%T 164128169205,2560224004884,40314178429707,639948824981928,

%U 10230035192533800,164541833894991240,2660919275605834701,43239781879996449825,705687913212419321800,11561996402992103418000,190100812111989146008641

%N 9*binomial(7*n+9, n)/(7*n+9).

%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=7, r=9.

%H Vincenzo Librandi, <a href="/A233907/b233907.txt">Table of n, a(n) for n = 0..200</a>

%H J-C. Aval, <a href="http://arxiv.org/pdf/0711.0906v1.pdf">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.

%H Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>

%H Wojciech Mlotkowski, <a href="http://www.math.uiuc.edu/documenta/vol-15/28.pdf">Fuss-Catalan Numbers in Noncommutative Probability</a>, Docum. Mathm. 15: 939-955.

%F G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=7, r=9.

%t Table[9 Binomial[7 n + 9, n]/(7 n + 9), {n, 0, 30}]

%o (PARI) a(n) = 9*binomial(7*n+9,n)/(7*n+9);

%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/9))^9+x*O(x^n)); polcoeff(B, n)}

%o (MAGMA) [9*Binomial(7*n+9, n)/(7*n+9): n in [0..30]];

%Y Cf. A000108, A002296, A233832, A233833, A143547, A233834, A130565, A233835, A233908.

%K nonn

%O 0,2

%A _Tim Fulford_, Dec 17 2013

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Last modified April 13 13:24 EDT 2021. Contains 342936 sequences. (Running on oeis4.)